Algebras And Representation Theory
The Peterson comparison formula proved by Woodward relates the three-pointed Gromov-Witten invariants for the quantum cohomology of partial flag varieties to those for the complete flag. Another such comparison can be obtained by composing a combinatorial version of the Peterson isomorphism with a result of Lapointe and Morse relating quantum Littlewood-Richardson coefficients for the Grassmannian to k-Schur analogs in the homology of the affine Grassmannian obtained by adding rim hooks. We show that these comparisons on quantum cohomology are equivalent, up to Postnikov’s strange duality isomorphism.
Quantum cohomology, Grassmannian, Affine Schubert calculus, k-Schur function, Littlewood-Richardson coefficients, Peterson isomorphism
Linda Chen, E. Milićević, and J. Morse.
"An Affine Approach To Peterson Comparison".
Algebras And Representation Theory.